Pith Number

pith:AU6PLYEV

pith:2013:AU6PLYEVL2EJ5ACMBUJJVXW7QL

not attested not anchored not stored refs pending

The subgroup membership problem in amalgamated products of finitely generated free groups

Andrew Duncan, Elizaveta Frenkel

arxiv:1305.4407 v2 · 2013-05-19 · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AU6PLYEVL2EJ5ACMBUJJVXW7QL}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:25:15.578982Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

053cf5e0955e889e804c0d129adedf82e4dea6b8362c2818b57344d5ee89cb32

Aliases

arxiv: 1305.4407 · arxiv_version: 1305.4407v2 · doi: 10.48550/arxiv.1305.4407 · pith_short_12: AU6PLYEVL2EJ · pith_short_16: AU6PLYEVL2EJ5ACM · pith_short_8: AU6PLYEV

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/AU6PLYEVL2EJ5ACMBUJJVXW7QL \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 053cf5e0955e889e804c0d129adedf82e4dea6b8362c2818b57344d5ee89cb32

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b75e3bca53b0ccd118b32723f3580bf164dd7deef92bcd9d680edf12a6fc12e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2013-05-19T19:54:46Z",
    "title_canon_sha256": "a90d7091e9da3f540fd5fda9f7dcef1da07f85d30319f8eec4d0467934367782"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1305.4407",
    "kind": "arxiv",
    "version": 2
  }
}